On groupoids with involutions and their cohomology

Abstract

We extend the definitions and main properties of graded extensions to the category of locally compact groupoids endowed with involutions. We introduce Real Čech cohomology, which is an equivariant-like cohomology theory suitable for the context of groupoids with involutions. The Picard group of such a groupoid is discussed and is given a cohomological picture. Eventually, we generalize Crainic's result, about the differential cohomology of a proper Lie groupoid with coefficients in a given representation, to the topological case.

46 pages, the abstract has been modified, typos fixed, minor corrections, and Examples 1.32 and 1.53 added

References in corpus (2)

• Type I D-branes in an H-flux and twisted KO-theory
• The ring structure for equivariant twisted K-theory